Beta Formula (Table of Contents)
 Beta Formula
 Calculate Beta by Correlation Formula
 Calculate Beta Manually
 Calculation of Beta for the stock profile
 Beta Calculator
 Beta Formula in Excel (With Excel Template)
Beta Formula
Beta is the very important element in the stock analysis it measures risk in stock or in the stock portfolio. Beta is very volatile as it depends on the stock market and we know very well that the stock market is very much volatile. Beta not only evaluate the risk associated with a particular stock but also used to evaluate the expected rate on returns and Discounted cash flow evaluation. Beta is the covariance of the return of an asset divided by variance of the return of the benchmark over a certain time period and formula for this can be written as:
Where,
 R_{e }= Stock Return
 R_{m }= Market Return
Calculation of Beta by above Beta Formula
Beta can be calculated using above beta formula by following below steps:
 Get past security price for an asset of the company.
 Get past security price for comparison benchmark.
 Calculate the percentage change periodically for both asset and benchmark.
 Calculate variance by VAR.S(Sum of all the percentage changes of the asset).
 Calculate Covariance by COVARIANCE.S(Sum of all the percentage changes of the asset, the Sum of all the percentage changes of the benchmark).
 Divide Covariance by variance to get the Beta.
Examples
Let’s see an example to calculate Beta.
A company has below asset and benchmark price from Jan2018 to Dec2018.
Date  Assets Price  Benchmark Price  Percentage of Change in Asset  Percentage of Change in Benchmark 
1Jan18  232  1274  0.92  0.15 
1Feb18  446  1460  0.34  0.24 
1Mar18  294  1110  0.09  0.24 
1Apr18  321  1376  1.27  0.04 
1Jun18  730  1316  0.11  0.01 
1Jul18  648  1300  0.08  0.04 
1Aug18  703  1351  0.04  0.03 
1Sep18  728  1396  0.05  0.03 
1Oct18  689  1440  0.68  0.2 
1Nov18  220  1148  1.71  0.09 
1Dec18  597  1247  1  1 
Then calculate the percentage of change in asset and percentage of change in the benchmark.
Variance is Calculated as:
Covariance is calculated as:
Beta is calculated as:
So, the value of Beta is 0.24 which company is less volatile than the market.
Calculate Beta by Correlation Formula
Beta formula in term of correlation can be written as:
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Where,
 σ_{e}= Standard deviation of returns of the benchmark
 σ_{m} = Standard deviation of returns of asset
Above formula is used to calculate Beta by dividing the standard deviation of returns of the asset by standard deviation of returns of benchmark which is multiply by correlation of asset return and benchmark return.
Now, let us calculate Beta by correlation formula.
Suppose an investor wants to invest in a company, he wants to calculate Beta of the company and compare it with S&P 500 EFT Trust correlation between two is 0.62, the standard deviation of returns of the company is 22% and standard deviation of returns of S&P is 30%.
 Beta = Correlation(R_{a }– R_{m}) *( σ_{e /} σ_{m})
 Beta = 0.62 * (0.22 / 0.30)
 Beta= 0.45
So, the value of Beta is 0.45 which company is less volatile than the market.
Calculate Beta Manually
Beta can be calculated manually by following below steps:
 Find the risk free rate
It is the rate of return on investment done.
 Find the rate of return of stocks and rate of return on market
If any of the value is in negative that will leads to a value of beta as negative which means loss.
 Find return on risk is taken on stock
It is the stock’s rate of return minus risk free rate.
 Find return on risk is taken on the market
It is the market’s rate of return minus risk free rate.
 Divide return on risk is taken on the stock by return on risk taken on the market
This will provide you value for Beta.
Let us an example to calculate Beta manually,
A company gave risk free return of 5%, the stock rate of return is 10% and the market rate of return is 12% now we will calculate Beta for same.
Return on risk taken on stocks is calculated using below formula
 Return on risk taken on stocks = Stock Rate of Return – Risk Free Return
 Return on risk taken on stocks = 10% – 5%
 Return on risk taken on stocks = 5%
Return on risk taken on Market is calculated using below formula
 Return on risk taken on Market = Market Rate of Return – Risk Free Return
 Return on risk taken on Market = 12% – 5%
 Return on risk taken on Market = 7%
Beta is Calculated using below formula
 Beta = Return on risk taken on stocks/ Return on risk taken on Market
 Beta = 5 /7
 Beta = 0.71
So, value for beta is 0.71 which company is less volatile than the market.
Calculation of Beta for the stock profile
Now, let us see a calculation of Beta for the stock profile.
Beta is calculated for stock and for a stock portfolio value of each stock Beta is added up according to their weights to create the portfolio beta. The formula for same is as follows:
The beta of Portfolio = Weight of Stock * Beta of Stock + Weight of Stock * Beta of Stock…so on
Let us see an example to calculate the same.
An investor has a portfolio of $100,000, the market value of HCL is $40,000 with a Beta value of HCL is 1.20, and market value of Facebook is $60,000 with Beta value is 1.50. The beta of the portfolio will be:
Weight of HCL is calculated as:
 Weight of HCL = 40,000 / 100,000
 Weight of HCL = 0.40
Weight of Facebook is calculated as:
 Weight of Facebook = 60,000 / 100,000
 Weight of Facebook = 0.60
Beta of Portfolio is calculated as:
The beta of Portfolio = Weight of Stock * Beta of Stock + Weight of Stock * Beta of Stock…so on
 Beta of Portfolio = (0.40*1.20) + (0.60*1.50)
 Beta of Portfolio = 0.48 + 0.9
 Beta of Portfolio = 1.38
The beta of the portfolio is 1.38, which means the stock is highly risky and volatile.
Beta Measurement and its Relation with Market
Value of Beta defines the risk associated with the company, Beta tells whether investment in the company is risky or not and how much it is depended on the market. Beta measures the stock rise in relation to the stock market. Beta value and its interpretation are as follows:
 If Beta = 1, then risk in stock will be the same as a risk in the stock market. It means the stock is volatile like the stock market.
 If Beta >1, then the level of risk is high and highly volatile as compared to the stock market.
 If Beta > 0 and Beta < 1, then the stock price will move with the market. However, the stock price will be less risky and less volatile.
Uses of Beta Formula
There are many uses of Beta and its formula and they are as follows:
 It helps in risk analysis of the stock.
 Beta helps to calculate rate on returns.
 It also helps in the evaluation of discounted cash flow.
 Beta provides a real picture of the investment portfolio.
Beta has some disadvantages as it depended on past performance but in reality past performance has no guarantee of future and it cannot give an accurate value. But, still, Beta is highly used by investment bankers and investors to calculate risk.
Beta Calculator
You can use the following Beta Calculator
Covariance  
Variance  
Beta Formula  
Beta Formula  = 


Beta Formula in Excel (With Excel Template)
Here we will do the same example of the Beta formula in Excel. It is very easy and simple.
You can easily calculate the Beta using Formula in the template provided.
Beta using the correlation formula is calculated as:
Return on risk taken on stocks is calculated as:
Return on risk taken on Market is calculated as:
Beta is Calculated using below formula
Weight of HCL is calculated as:
Weight of Facebook is calculated as:
Beta of Portfolio is calculated as:
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